reserve I for set,
  x,x1,x2,y,z for set,
  A for non empty set;
reserve C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,g,h,i,j,k,p1,p2,q1,q2,i1,i2,j1,j2 for Morphism of C;
reserve f for Morphism of a,b,
        g for Morphism of b,a;
reserve g for Morphism of b,c;
reserve f,g for Morphism of C;

theorem
  c is_a_coproduct_wrt i1,i2 & d is_a_coproduct_wrt j1,j2 & dom i1 = dom
  j1 & dom i2 = dom j2 implies c,d are_isomorphic
proof
  assume that
A1: c is_a_coproduct_wrt i1,i2 and
A2: d is_a_coproduct_wrt j1,j2 and
A3: dom i1 = dom j1 & dom i2 = dom j2;
  set I = {0,{0}}, F = (0,{0})-->(i1,i2), F9 = (0,{0})-->(j1,j2);
A4: c is_a_coproduct_wrt F & d is_a_coproduct_wrt F9 by A1,A2,Th79;
  doms F = (0,{0})-->(dom j1,dom j2) by A3,Th6
    .= doms F9 by Th6;
  hence thesis by A4,Th72;
end;
